Let's imagine an actor, a good Christian. As a part of his role of some pagan, he prays to Zeus or other ancient deity on stage. He just plays the role and there is no inclination to Zeus behind his words and gestures (he may even pray to the true God in heart while playing the scene), but the words and gestures are the same as used by real pagans many centuries ago.
That's what I call "actor's idolatry" - the action as seen from outside and without knowledge of context seems to be idolatry, but there's no intention to sin.

I know some would say it is idolatry, some not, and it depends on circumstances too. Biblical reasons why this should be seen as a case of idolatry are quite frequent in Old Testament (for example Ex 23:13). But what are reasons from Bible (or tradition) that "actor's idolatry" isn't real idolatry?

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1 Answer
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You are not describing something that is traditionally considered to be idolatry. However, you may be describing the sin of scandal (beliefs may vary on what constitutes "leading others into sin", but I understand that you're not asking us to get into that).

The Catechism actually addresses this almost directly, in the following:

2113 Idolatry not only refers to false pagan worship. It remains a constant temptation to faith. Idolatry consists in divinizing what is not God. Man commits idolatry whenever he honors and reveres a creature in place of God, whether this be gods or demons (for example, satanism), power, pleasure, race, ancestors, the state, money, etc. Jesus says, "You cannot serve God and mammon." Many martyrs died for not adoring "the Beast" refusing even to simulate such worship. Idolatry rejects the unique Lordship of God; it is therefore incompatible with communion with God.

Even the simulation of idolatry, in order to escape death during persecution, is a mortal sin, because of the pernicious falsehood it involves and the scandal it causes. Of Seneca who, against his better knowledge, took part in idolatrous worship, St. Augustine says: "He was the more to be condemned for doing mendaciously what people believed him to do sincerely".

The point here is that the "simulation of such worship" is marked as distinct from the actual worship (idolatry), and then explained to be a matter of doing what others believe is done sincerely. So the traditional understanding of idolatry, re-iterated there by St Augustine, is that it requires sincerity. In the same way, our worship of God also requires sincerity, and not merely "outward displays".

So acting out or demonstrating how pagans worshipped is not the sin of idolatry. (Except when it is: if you know you are particularly prone to falling into idolatry, or your acting style very much involves you "getting into the role" mentally, then this may not be the role for you).

But there is actually another part to your question. Most people don't really believe that what is done in the context of theatre or film is done sincerely, except perhaps children (...there was a time when I thought a certain actor really had a disability due to a convincing character portrayal). But what you go on to describe as "actor's idolatry" (action as seen from outside without knowledge of context) is traditionally considered not to be the sin of idolatry, but the sin of scandal.

2284 Scandal is an attitude or behavior which leads another to do evil. the person who gives scandal becomes his neighbor's tempter. He damages virtue and integrity; he may even draw his brother into spiritual death. Scandal is a grave offense if by deed or omission another is deliberately led into a grave offense.

There really won't be any basis for this not being a sin. Scripture is very clear, see for example Luke 17:1-2, Proverbs 28:10. The only thing in dispute is whether certain things count as leading others into sin - and that can be a pretty big dispute among people.